To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
splitting theorems due to Zaicev and Duan proving the following result. Let
G be a locally soluble FC-hypercentral group and let
A be a periodic artinian ℤG-module. If
A has no finite ℤG-submodules then any
extension E of A by G
splits conjugately over A.
Meningo-encephalocoeles of the skull base may present as spontaneous cerebrospinal fluid rhinorrhoea or acute meningitis. Previous approaches to midline skull base lesions have been either intracranial, via a craniotomy, or by transfacial or endoscopic extracranial approaches. This paper presents an alternative approach to lateral sphenoid sinus encephalocoeles through a Le Fort I osteotomy approach.
Fitting classes and their associated injectors have been considered
in a number of
classes of locally finite groups [9, 8, 4,
5]. In particular, Dixon has considered the class
[Lfr ] of countable locally finite groups with min −p for
all primes p. He has shown that
if the [Lfr ]-group G is radical (that is, it has an ascending
locally nilpotent series) then
G has locally nilpotent injectors, any two of which are
isomorphic. Question 7.4.7 in
 asks whether the restriction of being radical
can be removed in this result.
Auricular haematoma is a problem frequently complicated by recurrence due to failure to apply adequate pressure over the pinna following simple drainage. We describe a simple method of splinting the pinna using silicone putty which overcomes this problem.
We introduce a definition of a Schunck class of periodic abelian-by-finite soluble groups using major subgroups in place of the maximal subgroups used in Finite groups. This allows us to develop the theory as in the finite case proving the existence and conjugacy of projectors. Saturated formations are examples of Schunck classes and we are also able to obtain an infinite version of Gaschütz Ω-subgroups.
Palatal myoclonus is defined as a continuous, rhythmic contraction of the palatal musculature. Reverberant neuronal activity in a region of the brain stem known as the Guillain-Mollaret triangle is believed to underlie this condition.
We present a case of palatal myoclonus which could be abolished, by anterior neck flexion. The pathology and management of this condition is briefly discussed.
Atomically ordered PdAgH and PdCuH hydrides synthesized in an atmosphere of gaseous hydrogen at P = 3 GPa were studied by inelastic neutron scattering. The results showed a large difference between the Pd-H, Ag-H and Cu-H interactions. Values of 93 and 116 meV were predicted for the local H vibrations in dilute Ag-H and Cu-H solid solutions.
The authors together with M. J. Karbe [Ill. J. Math. 33 (1989) 333–359] have considered Fitting classes of -groups and, under some rather strong restrictions, obtained an existence and conjugacy theorem for -injectors. Results of Menegazzo and Newell show that these restrictions are, in fact, necessary.
The Fitting class is normal if, for each is the unique -injector of G. is abelian normal if, for each. For finite soluble groups these two concepts coincide but the class of Černikov-by-nilpotent -groups is an example of a nonabelian normal Fitting class of -groups. In all known examples in which -injectors exist is closely associated with some normal Fitting class (the Černikov-by-nilpotent groups arise from studying the locally nilpotent injectors).
Here we investigate normal Fitting classes further, paying particular attention to the distinctions between abelian and nonabelian normal Fitting classes. Products and intersections with (abelian) normal Fitting classes lead to further examples of Fitting classes satisfying the conditions of the existence and conjugacy theorem.
The phonon spectra of pristine fullerene, superconducting K3C60 and saturation-doped Rb6C60 measured by inelastic neutron scatteringin the energy range 2.5 - 200 meV at low temperatures reveal substantial broadening of five-fold degenerate Hg intramolecular vibrational modes both in the low-energy radial and the high-energy tangential part of the spectrum. This provides strong evidence for a traditional phonon-mediated mechanism of superconductivity in the fullerides but with an electron-phonon coupling strength distributed over a wide range of energies (33-195 meV) as a result of the finite curvature of the fullerene spherical cage.
A group G is said to be quasi-injective if, for each subgroup H of G and homomorphism θ:H→G, there is an endomorphism such that . It is of course well known that the category of groups does not possess non-trivial injective objects and so we consider groups satisfying the weaker condition of quasi-injectivity.
Finite soluble groups in which all the Sylow subgroups are abelian were first investigated by Taunt  who referred to them as A-groups. Locally finite groups with the same property have been considered by Graddon . By the use of Sylow theorems it is clear that every section (homomorphic image of a subgroup) of an A-group is also an A-group and hence every nilpotent section of an A-group is abelian. This is the characterization that we use here in considering groups which are not, in general, periodic.
The Carter subgroups of a finite soluble group may be characterised either as theself-normalising nilpotent subgroups or as the nilpotent projectors. Subgroups with properties analogous to both of these have been considered by Newell (2, 3) in the class of -groups. The results obtained are necessarily less satisfactory than in the finite case, the subgroups either being almost self-normalising (i.e. having finite index in their normaliser) or having an almost-covering property. Also the subgroups are not necessarily conjugate but lie in finitely many conjugacy classes.
If is a saturated formation of finite soluble groups and G is a finite group whose -residual A is abelian then it is well known that G splits over A and the complements are conjugate. Hartley and Tomkinson (1975) considered the special case of this result in which is the class of nilpotent groups and obtained similar results for abelian-by-hypercentral groups with rank restrictions on the abelian normal subgroup. Here we consider the super-soluble case, obtaining corresponding results for abelian-by-hypercyclic groups.
Further results from the theory of finite soluble groups are extended to the class of locally finite groups with a satisfactory Sylow structure. Let be a saturated U-formation and A a -group of automorphisms of the -group G. A is said to act -centrally on G if G has an A-composition series (Λσ/Vσ; σ ∈ ∑) such that A induces an f(p)-group of automorphisms in each p-factor Λσ/Vσ. We show that in this situation A is an -group, thus generalising the result of Schmid . Associated results of Schmid and of Baer are also extended to the infinite case.
We give a general method for constructing subgroups which either cover or avoid each chief factor of the finite soluble group G. A strongly pronorrnal subgroup V, a prefrattini subgroup W, an -normalizer D and intersections and products of V, W, and D axe all constructable. The constructable subgroups can be characterized by their cover-avoidance property and a permutability condition as in the results of J. D. Gillam  for prefrattini subgroups and -normalizers.
It is a well known theorem of Gaschütz (4) and Schenkman (12) that if G is a finite group whose nilpotent residual A is Abelian, then G splits over A and the complements to A in G are conjugate. Following Robinson (10) we describe this situation by saying that G splits conjugately over A. A number of generalizations of this result have since been obtained, some of them being in the context of the formation theory of finite or locally finite groups (see, for example, (1), (3)) and others, for example, the recent and far-reaching results of Robinson (10, 11) being concerned with groups which are not necessarily periodic. Our results here are of the latter type.
W. Gaschutz  introduced a conjugacy class of subgroups of a finite soluble group called the prefrattini subgroups. These subgroups have the property that they avoid the complemented chief factors of G and cover the rest. Subsequently, these results were generalized by Hawkes , Makan [14; 15] and Chambers . Hawkes  and Makan  obtained conjugacy classes of subgroups which avoid certain complemented chief factors associated with a saturated formation or a Fischer class. Makan  and Chambers  showed that if W, D and V are the prefrattini subgroup, 𝔍-normalizer and a strongly pronormal subgroup associated with a Sylow basis S, then any two of W, D and V permute and the products and intersections of these subgroups have an explicit cover-avoidance property.